There exists a utilitarian tradition a la Sidgwick of treating equal generations equally. Diamond showed that no social evaluation ordering over infinite utility streams satisfying the strong Pareto principle, Sidgwick's equity principle, and the axiom of continuity exists. We introduce two versions of egalitarianism in the spirit of the Pigou-Dalbon transfer principle and the Lorenz domination principle, and examine their compatibility with the weak Pareto principle in the presence of the weak continuity axiom. The social evaluation relation is assumed neither complete nor fully transitive, yet Diamond's impossibility strenuously resurfaces.We introduce several distinct notions of equity as no-envy into the overlapping generations economy formulated by Samuelson (1958). No-Envy in Overlapping Consumption requires that for each time period, no person prefer the bundle of any other person who lives in the same period. No-Envy in Lifetime Consumption states that no person should prefer the lifetime consumption plan of any other person. Equity in Lifetime Rate of Return requires that the lifetime rate of return (Cass and Yaari, 1966) be equal for all persons. For each of the three notions, we characterize allocations satisfying it, and clarify logical relation among these conditions. We also examine existence of a stationary allocation that attains maximal utility under No-Envy in Lifetime Consumption.